**Assessment vs. Evaluation:What's the Difference?**

by Mona Lasley

When teachers hear the word *assessment, *it is often confused with evaluation, which is often done by individual testing of students. How do teachers differentiate between the two ideas?

Evaluations are usually written and are not necessarily used to diagnose the problems of a student. They come at the end of a series of lessons or at the end of a unit, and are typically used to rank student performance. This ranking is reported in the grade book as a percentage or number of points which is then translated to an A-F scale. The evaluative material may be reviewed in class, but it is not generally discussed in very much depth, nor is it used as a teaching tool.

By the time a student is evaluated, the instruction is over for much of the material covered, and the teacher has moved on to another topic. If the majority of students do poorly, the teacher may place blame on the students and go on, or may stop and re-teach. Often, little is done to find the real cause for the failure of the student. If the teacher sees a nice Bell Curve, s/he may feel satisfied that a good job was done and go on to the next lesson, leaving those students at the bottom of the curve to drown in their misunderstandings!

**Evaluations are typically used to rank student performance.Assessments give information on the student's progress.**

An assessment is an activity which gives us information about the performance and understanding of a student. It** **may take the form of a written piece of work, a collection of student work, a project, an interview or discussion with a student, or an observation.

The assessment gives** **clues to the way the student is thinking and an awareness of how the student approaches difficult problems. It reveals whether the student has made a connection between what s/he already knows in mathematics and the new ideas on which s/he currently is working. It also gives a measure of the progress s/he is making in solving problems on which new ideas must be used. In short, it** **helps the teacher to help the student. The teacher and student both analyze the work that was done.

Some important life-skills** **may not be evaluated, but may be assessed. Persistence in working on difficult problems is a skill which teachers attempt to encourage, but rarely evaluate. It may, however, be observed and assessed. The teacher may meet individually with the student to plan ways in which s/he may become more persistent when faced with mathematical challenges. Cooperation with other students is also important and is a skill which may be observed and assessed. These are skills which may also be self-assessed by the student. Students may even write their own plans for improvement!

There are places in the mathematics classroom for both assessment and evaluation. Parents, students, and the public need evaluations as a "measuring stick" for knowing the student's place in mathematics. We all need to know our place in the world. However, we also need a means of advancing in the world. Assessment helps us to improve our skills and change our place on the "measuring stick." It helps us to grow mathematically!

Mona Lasley teaches at Natomas Junior High and co-authored the CPM Assessment Handbook. It is full of ideas and insights, designed for and by CPM classroom teachers. It came, either in hard copy or on disk, with your Teacher Version. If you need a copy, fax or e-mail Jane Bradley.

**Look Here!**

**Advice for the CPM classroom teacher**

*Some of my students won't check their homework. I put the answer key in the front of the room at the beginning of the period but only a few check their work. What can I do?*

I like to give a "pop" homework quiz once per week. I usually fold a piece of paper into four sections and copy one homework problem on each fourth of a piece. I then photocopy the page and cut them up. I put all four quizzes at each table so the first students into class have their "pick of the litter."

They are allowed to use their notes and have until a minute or two after the tardy bell to finish. I instruct them to turn their paper over when they finish and I collect the ones that are turned over (walking around the room the entire time that the quiz is going on).

The added advantage is that you can take roll the first minute or two of the period and when you're done, collect the papers. I select problems from different days so that the students will want to make sure that they consistently work the problems correctly and get the correct answers.

*I really value the necessity of circulating around the classroom but, to be honest, my feet really hurt by the end of the day. Is there anything I can do besides soaking my feet?*

I solve this problem by keeping a few spare desks or chairs strategically located around the room. I slide one into a group and get to "sit a spell" and mingle with my students. This actually lets me become part of the team. It also lets me get to meet the students at their eye level.

**Video Resources Help Bridge to the Standards**

by Ruth Tsu

TEACHING MATH: A Video Library, 9-12 provides mathematics educators with tools to implement the NCTM Curriculum and Evaluation Standards. These unscripted video pictures of classes give teachers, administrators, parents, and policy-makers a first-hand look at the changes happening in mathematics instruction.

William Masalski, one of the core advisors to the project said, "The TEACHING MATH videos actually show teachers in classrooms at various stages trying to implement the Standards. Some teachers are well along the way, others are just beginning. You're taken right into a classroom and you're able to see the teacher interacting with students."

These videos can be especially useful for a teacher contemplating change, a teacher whose principal or students' parents do not understand why math is changing, or a master teacher with student teachers.

This video library was developed by the Educational Programming Group of the Special Telecommunications Services division, WGBH Educational Foundation. Funding was provided by the Annenberg Foundation/Corporation for Public Broadcasting–Elementary and High School Project for Mathematics and Science.

By now I am sure you are wondering how you can arrange to see these videos? There are three ways for you to do this.

#1. Purchase the entire library of ten VHS cassettes plus a three-ring guidebook to use with the videotapes, at a cost of $250. You can order a free preview, the series or a catalog by calling 1-800-965-7373.

#2. If your school or district has the necessary equipment, you can tape the series, Monday, April 7 - Wednesday, May 14. You will need Satellite: Galaxy 4, Transponder 12 Ku band 11939.375 MHz, polarity: horizontal. For technical help, call 1-800-528-7749. They videos will be broadcast at 11:00 AM on Mondays and repeated at 4:00 PM and again at 6:00 PM on Wednesdays (all times are Eastern Time).

#3. Call your local public television station and ask whether or not they will broadcast the series offered by Annenberg/CPB Channel. Expressing your interest in their doing so cannot hurt the chances of their doing so!

For more information: E-mail: acpbtv@learner.org or phone: 1-800-556-4376 or fax: 1-617-252-5709

Write: Annenberg/CPB Channel, c/o MCET, 1 Kendall Square, Building 1500, Cambridge, MA 02139

If you choose #2 or #3, you may like to know that the material in the guidebook can be found on the internet at: http://www.learner.org/k12/acpbtv

**Mid-Year Study Team Suggestions**

Here are a few suggestions that have been offered in previous years.

- To help keep students on task, give credit twice: once near the end of the period for sustained effort on the developmental problems; again when students enter class the next day for completing the assignment.
- To address the problem of students who try to ride the coattails of better students, try arranging groups by effort and application. Put the top four workers in one group and so on down to the least hard-working four in a group. This may only work for a short time, but those who have tried it say it has helped to jump-start the students.
- To correct erroneous conjectures, intervene with questions as appropriate: "Did you verify your conjecture?" "Does this conclusion work in this problem (when you know it doesn't--it then becomes a counter-example)?" "Let's take a closer look at your work... (followed by appropriate questions)." And the ever popular "Let's reread the question together." These types of questions respect the students' work and make your role more that of a partner than a judge.
- Switch to pairs if socializing or general behavioral problems make larger grouping impractical.

When to intervene? There will be times when the whole class is confused or their work is seriously flawed. This may be a good time for a full class focus. Questioning techniques like those outlined above help to focus students on a problem. This may also be a time for some prescriptive lecturing to build a bridge that the students cannot. Be careful, though! These are times that can lead us to intervene too early. Some struggle is necessary and a precursor to learning.

**Becoming a CPM Teacher: One Teacher's Experience**

by Jack Nunes

A funny thing happened when I opened the last newsletter: I found the CPM web site and said "Hello!" to Naomi Tsu. Now I find myself writing for the newsletter!

This all started two and a half years ago when I began teaching what at first seemed to be a curious approach to Algebra 1: CPM Math 1. However, I was an experienced Math Renaissance teacher and CPM was somewhat similar to that approach to teaching math. The first year my 8th grade class was animated, noisy and fun. We were unable to finish the book, but by the end of the year the students had mastered an array of "math attack skills" and a basis for high school math. That year sure beat the "memorize--repeat--forget" experience of most other math courses I've taken and taught.

Last year was better. I was more efficient in managing the lessons, so their flow seemed more natural. These students were also noisy yet deadly serious about learning algebra. They barely tolerated my lame jokes!

By the end of the year I knew my two-year sojourn was worthwhile. The Golden State Exam (GSE) results for Algebra 1 were phenomenal: my class had 20% at level six, 23% at level five, and 20% at level four, compared with the state averages of 7.9, 8.6, and 11.9 respectively. I was especially proud of these results given that we are a Title I school with a large number of ESL students, many of whom are enrolled in Algebra 1.

This year, however, is one of the best I've had as a teacher. I don't know if it's me, the class, or what, but just about every lesson works well. I do know that I am now able to anticipate roadblocks and help students to reach consistent "A-Ha!" experiences. My use of the program feels natural and simple. Now the kids just dig in and get the work done. They really work at understanding what they are doing and balk at taking "help" from students or me that just offers answers or shortcuts. What a pleasant change!

**Kids just dig in and get the work done. They really work at understanding what they are doing and balk at taking "help" that just offers answers or shortcuts.**

I guess my experiences show that it does take time to make changes, but that change also can bring about wonderful results. I'm really excited about getting the second edition of Math 1 for my class next year.

Jack Nunes is a teacher at Fern Bacon Middle School in the Sacramento Unified School District.

**NAEP Scores: What's Behind the Headlines?**

by Brian Hoey

The media reported the results of the NAEP test (National Assessment for Educational Progress, a voluntary test given by the federal government to a random sample of 4th, 8th, and 12th graders in 42 states, Guam and the District of Columbia) on February 28th and, as expected, the scores were not satisfactory. In particular, the headlines focused on California's low ranking in 4th and 8th grades: "State Ranks Near Bottom on Math Skills Test" (Los Angeles Times), "State Kids Lag in Math Skills" (San Francisco Chronicle), "The Sad State of Math Skills" (San Jose Mercury News), and "Math Skills on the Minus Side" (Sacramento Bee). The 4th grade scores tied for 40th place; 8th grade scores ranked 31st.

Certainly the current status of math education achievement–both nationally and in California–is unacceptable. But what the headlines and articles neglect to say is that virtually all of the students tested have used traditional materials, NOT reform math curricula. This was also true of the classes studied in the Third International Math and Science Study report of last November (TIMSS,10/96).

In addition, the rush to condemn California students' performance in terms of the state rankings and scores alone distorts the complexity of the math education issue. The S.F. Chronicle published the 8th grade scores for all states. Yes, California ranks 31st, but this is only 4.2% lower than top-scoring North Dakota and 6.6% higher than the lowest scoring District of Columbia.

**Any plan to improve math instruction must contain a substantive teacher inservice component**

Furthermore, the articles cited above note that lower scores seem to be related to issues such as class size, an area where California also ranks among the lowest states in the nation. The other states with scores just above and those lower than California are located in the South, Hawaii, Guam and D.C. Top-scoring states (North Dakota, Maine, Minnesota, Iowa, Montana, Wisconsin and Nebraska) do not face the formidable challenge that ethnic diversity brings to California classrooms, namely, as many as forty language groups within a single large district!

Again, we wish to emphasize that no one can or should be pleased with the NAEP scores beyond noting that they are increasing (an average of 1%), albeit not nearly enough. These test results, coupled with the TIMSS report, reinforce the mandate of the State Board of Education that California math instruction include a balance of basic skills, conceptual understanding and problem solving.

In particular, these studies indicate that any plan–and hope -- to improve math instruction must contain a substantive teacher inservice component. Otherwise, the best standards, curriculum materials, and assessment programs will never achieve their goals.

**Helping the Community Understand Change in Mathematics Education**

If you watch the nightly news on TV or read a daily newspaper, you are certainly aware of how politicized education has become. Politicians address the issue, columnists visit the topic, and editors comment about it regularly. Much of what these people say is shaped by the input they receive from the public. This is why we encourage you to take the opportunity to inform the public about math education: how and why it is changing, what is different, and what is the same.

It is particularly important to point out that in the CPM program the math never left! CPM is about offering students multiple ways to learn procedures, concepts and problem solving strategies. CPM believes that students need to develop and work with ideas in order to understand what they do with them and why they do it. The math of previous generations–with at best a 50% success rate–is not enough for the students of the 21st century.

**It is particularly important to point out that in the CPM program the math never left!**

CPM wants more students to learn more math by being active participants in the learning process. Thus, students use study teams, class discussions, teacher lectures, presentations and practice to master college prep mathematics. Writing letters to your paper is important. How will editors and reporters learn about the complexity of the math education issue without input from experts like yourself? When articles and editorials appear in your local paper–whether you agree with them or not–take the time to write 100 to 300 words to the editor. Be clear and succinct; your points are best made by using personal accounts from your classroom to support them. Remember: get the letter off within three days after the article or editorial appears. Letters are read, even if they are not published. E-mail, fax or U.S. mail are acceptable means of sending your letter.

**Other Suggestions for Community Education**

When appropriate, explain to students why you are doing something and the advantages it offers.

Take advantage of every parent event to show what your students are doing. Emphasize the mathematics of your examples, that the courses are fundamentally the same as other such courses, and why the methodology is effective with more students.

Be certain that every administrator is educated about CPM.

Conduct "CPM Information Nights" to explain CPM's philosophy and goal of more mathematical learning for more students. Demonstrate some vivid, representative problems, have parents do a problem or two, and answer their questions.

Ask parents and students to write letters to the appropriate administrator(s) expressing why they find CPM to be an improvement over prior math experiences.

**Applications to Join the Teacher-Leader Support Team**

Approximately 150 CPM teachers comprise the CPM leadership. These teachers attend a leadership institute each summer that helps them prepare to conduct the course workshop series and to support new CPM teachers with parent information nights and the like.

Teacher-Leaders mentor new CPM teachers and occasionally give presentations to school math departments, administrators and school boards. Regional coordinators and special projects coordinators are also drawn from this group.

If you would like to provide leadership in the implementation of the CPM program, request an application and additional information by faxing (916) 444-5263 or e-mailing (bradley@cpm.org) Jane Bradley. We especially encourage applications from teachers who have experience with district mentoring, workshop presentations, or California Math Project participation. Applicants are expected to complete a brief application, answer a few short essay questions about their math experience and why they want to be Teacher-Leaders, submit 2 letters of recommendation and be interviewed by a current Teacher-Leader. **Applications are due by April 15th.**

This year's Summer Leadership Institute will be June 19-21 in Sacramento and June 26-28 in Santa Ana. Teacher-Leaders attend the institute nearest their home.

**Adoption Reminder**

CPM has been successfully implemented in classes of teachers who choose to use it and who are willing to try some different approaches to learning mathematics. CPM does not support mandating that unwilling teachers use any curriculum–CPM or traditional.

**NCTM Regional Conference in San Jose**

It was nice to talk with so many enthusiastic CPM teachers at the CPM Exhibitors Booth! We were particularly pleased to hear that CPM classes continue to receive substantially more awards on the Golden State Exam than traditional classes in pre-CPM years and/or when compared to traditional classes in the same school. This has been a consistent, widespread trend all over the state and in every kind of school and class–GATE to Title 1–for the past four years.

Several teachers (who were in some cases also parents of CPM students) also shared concerns about how some of their colleagues are implementing the program. Thus, we remind you of a few key elements that should be part of a CPM classroom. CPM teachers:

- Circulate among the students while they are working in study teams;
- Have an obligation to help students who have questions to get back on track toward a successful solution. While asking students questions that will accomplish this end is the preferred approach, sometimes students need direct assistance–either a simple answer or a clarifying demonstration;
- Make solutions available to students on a regular and timely basis; and
- Employ a variety of methodologies to help students discover, summarize, consolidate, and internalize concepts and procedures. Lecture, class discussion, student presentations, posters, lab work (group time), individual student work and review/summarizing are all important in the CPM classroom.

**Math 1 Second Edition Update**

The preliminary second edition of Math 1 has been well-received!

Teachers using it like the rearranged sequence of topics and the new theme problems. The inclusion of highlighted boxes for main ideas and examples has helped both parents and students tie the text's developmental approach to the investigations' expected outcomes.

The managing editor informs us that units 0-6 have been polished in light of suggestions from the pilot team. We expect to do some rewriting of Unit 2; blacklines of the revised unit will be made available to those classrooms that use the preliminary edition this year. We will also enhance the visual appeal of the text with considerably more art work, new covers, and additional resources for projects and extensions. Finally, we will integrate the new Student Study Guide into the text itself.

Based on the reviews of the piloters and other teachers who are using the preliminary second edition, we strongly recommend that you replace the first edition whenever you reorder books. To this end, we will hold the price to just a dollar more than last year$16.00 per set. If you are replacing books for some of your students (for example, you need to order seventy replacement books due to damage and loss), order the second edition and use those books in two classes while the remaining classes use the first edition. We expect to have the first volume to the printer by the end of June and the second volume completed shortly thereafter. Books should be available for delivery by the third week of July for those on year-round schedules. Once again we will provide blackline masters for schools that need the first unit or two in advance of delivery.

Several of you have asked for the opportunity to attend a short workshop that will explain the difference between the first and second editions. We are currently working with Teacher-Leaders to develop a three hour, Saturday morning workshop that we hope to offer in several sites around the state in late April and early May. Details will be announced in the next mailing (early April).

**Homework Management Tips**

This work is for the student's benefit and is the student's responsibility. Your role shifts in CPM from enforcer to resource manager.

- The best method we have seen provides complete teacher-written solutions for each of the previous lesson's problems. Each group gets at least one copy of the solutions as the students enter the room. Some students will want to take these home to study. Fine! In this way, every problem in the book becomes an example after students have had a chance to consider them. Handwritten solutions are fine. Teachers in a school can share this work by week or by unit. Remember: do this once, and you have them ready for future years.
- Plan teacher-led homework review for the latter part of class. You will have had time to circulate and see what, if any, general concerns or difficulties are common to the class.
- "Grade" homework as full, half, or no credit. Circulate and record this during the first five minutes of class. Hopefully recording who does not have the work done will be faster than marking everyone who does! Focus on one or two problems to get an idea of how everybody did. Responsibility to correct homework is the students' if you use the method described in the first check mark above.
- Collect all the papers and check the same problem on each.

**In Memorium**

On January 23rd, we lost one of our colleagues. Li Oi Yu, an ESL/Math teacher at Washington High School in San Francisco, was lost in a tragic accident, along with her husband Louis, when their van went over Devil's Slide. Li Oi taught at Washington for the last fourteen years. She was a dedicated professional, a great mother to her four children and a kind-hearted person. She will be missed by all of her colleagues and students. Li Oi's legacy will live on through all the lives she touched and also via the Louis and Li Oi Yu Memorial Scholarship Fund at Washington High School.

written by Tom Swartz

To be added to the News You Can Use mailing list, send a request by fax (916-444-5263) or e-mail bradley@cpm.org

Executive Editor: Brian Hoey

Editor: Judith Kysh

March contributors: Joe Governale, Mona Lasley, Jack Nunes, Ruth Tsu

We welcome your comments and suggestions:

Production Manager: Brian Hamada

e-mail: bhamada@cpm.org

*Thanks to all!*